Final answer:
In hypothesis testing, the assumption that allows a conclusion to be properly drawn usually involves rejecting or failing to reject the null hypothesis based on the p-value compared to the level of significance. Larger sample sizes are generally more reliable, though small samples can still be informative in certain contexts. A hypothesis cannot be definitively proven but can be strongly supported by evidence.
Step-by-step explanation:
The student's question regarding hypothesis testing relates to determining which assumption allows a conclusion to be properly drawn. When conducting a hypothesis test, especially with matched or paired samples, option 'b' (Two measurements are drawn from the same pair of individuals or objects) and option 'c' (Two sample means are compared to each other) are both true.
In hypothesis testing, a null hypothesis (H0) is typically tested against an alternative hypothesis (Ha). The level of significance (α) is a threshold used to determine whether there is sufficient evidence to reject the null hypothesis. If the p-value is less than α, the null hypothesis is rejected.
Regarding sample size, while larger samples provide more reliable results, small samples may be necessary in certain contexts, such as with rare medical conditions. However, when the sample size is small, care must be taken before generalizing the results to the entire population. Ultimately, no hypothesis can be proven conclusively, but strong and consistent evidence can make it more likely to be true.